
/*
** Copyright (c) 2012 The Khronos Group Inc.
**
** Permission is hereby granted, free of charge, to any person obtaining a
** copy of this software and/or associated documentation files (the
** "Materials"), to deal in the Materials without restriction, including
** without limitation the rights to use, copy, modify, merge, publish,
** distribute, sublicense, and/or sell copies of the Materials, and to
** permit persons to whom the Materials are furnished to do so, subject to
** the following conditions:
**
** The above copyright notice and this permission notice shall be included
** in all copies or substantial portions of the Materials.
**
** THE MATERIALS ARE PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
** EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
** MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
** IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
** CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
** MATERIALS OR THE USE OR OTHER DEALINGS IN THE MATERIALS.
*/


#ifdef GL_ES
precision mediump float;
#endif
varying vec4 color;

void main (void)
{
    const float M_PI = 3.14159265358979323846;
    float c = 2.0 * M_PI * ( fract(abs(color.r)) - 0.5 );
    float sign =  1.0;
    float cos_c = -1.0;
    float fact_even = 1.0;
    float fact_odd  = 1.0;
    float sum;

    // At this point c is in the range [-PI, PI)

    // Taylor-Maclaurin series expansion for cosine
    //
    // Apply the property that pow(a, b + c) = pow(a, b) * pow(a, c)
    // and the property that 1.0/(a*b) = 1.0/a * 1.0/b
    // to make sure no register ever overflows the range (-16384, +16384)
    // mandated for mediump variables.

    for(int i = 2; i <= 10; i += 2)
    {
        // fact_even will hold at most the value 3840.
        fact_even *= float(i);

        // fact_odd will always be smaller than fact_even
        fact_odd  *= float(i-1);

        // pow(c, float(i/2)) takes at most the value pow(PI, 5), which is approx. 306
        // abs(sum) is at most PI/2.0
        sum = sign * pow(abs(c), float(i/2))/fact_even;

        // abs(sum/fact_odd) is at most PI/2.0
        // cos_c is always bound in the range [-1.0, 1.0)
        cos_c += pow(abs(c), float(i/2))*(sum/fact_odd);

        sign = -sign;
    }

    gl_FragColor = vec4(0.5 * cos_c + 0.5, 0.0, 0.0, 1.0);
}
